Given: the point C=(1,2,1) and
the ellipsoid E defined by
(x/7)^2 + (y/3)^2 + z^2 = 1.
Find the point A on E that is closest to C
and the point B on E that is farthest from C.
Find the distances d(A,C) and d(B,C).
Hint: the squared distance from (x,y,z) to C
is a much easier objective function to work with
than the distance. If A minimizes squared
distance to C, then it will also minimize
distance to C. If B maximizes squared distance
to C, then it will also maximize distance to C.
Remember, the textbook has lots of examples
(section 4.7). My spring 2017 course materials
also have examples (e.g. solutions to HW30).
And my fall 2016 course materials, and...